Focal Point
Focal Point is a critical concept in optics, referring to the specific point where light rays converge after passing through a lens or reflecting off a mirror. The distance from the center of the lens to this focal point is known as the focal length, which varies based on the lens's curvature. Understanding focal points is essential for applications in various optical devices, such as cameras and telescopes, where accurate image formation is necessary. Lenses can be either convex, which converge light to a real focal point, or concave, which diverge light, creating a virtual focal point. These interactions of light are influenced by refraction, a phenomenon that occurs when light transitions between different media, like air and glass. Additionally, imperfections in lenses result in a "circle of confusion," where light does not converge perfectly, affecting image sharpness. This aspect is particularly relevant in photography, where depth of field plays a role in determining which parts of an image appear in focus. Overall, the focal point and related optical principles are foundational for understanding how light behaves in lens systems.
Focal Point
FIELDS OF STUDY: Optics
ABSTRACT: The properties of lenses are determined by the curvature of their surfaces and the changes in the behavior of light as it passes through the lens medium. In most applications, the rays of light passing through a lens are bent so that they comes together in a single point, called the focal point. At this point, an object viewed through the lens is said to be "in focus," usually as an enlarged image for easier viewing.
PRINCIPAL TERMS
- aperture: an opening of a specific dimension designed to admit light into a lens or other optical system.
- circle of confusion: an imperfect image produced by a lens due to the rays of light passing through it not converging at a perfect point.
- concave: having surfaces that curve inward, like a bowl.
- convex: having surfaces that curve outward, like a ball.
- focal length: the distance from the center of a lens or curved mirror to the focal point.
- optics: the science of the interaction of light with lenses and mirrors.
- refraction: the change in direction of a light ray when it passes from one medium to another, such as from air to water.
Light and Matter
Most solid matter is opaque and prevents the passage of light through it. Materials such as glass are transparent and allow light to pass through. The transparency of a material may vary depending on the wavelength of the light. Crystalline sodium chloride (table salt), for example, is completely transparent to infrared but not entirely transparent to all wavelengths of visible light. The study of the behavior of light as it interacts with various forms of matter, such as glass formed into lenses, is called optics.
Because glass is transparent to visible light, it is an ideal material for optical lenses. Typically, light enters an optical device through an aperture and passes through the lens or lenses before being observed, as in a telescope, or creating a lasting image, as in a camera. On the other side of the lens, the light rays bend so that they all converge at one point, called the focal point
Properties of Lenses
When light travels from one medium to another, its direction of motion changes. This is called refraction. This effect can be observed by placing a straw in a glass of water. The portion of the straw that is above the water appears to point in a different direction than the portion below the water. This is because air and water have different refractive indexes. A refractive index is a dimensionless measure of how much light is bent by a particular material.
The same effect operates when light passes from air into glass. The rays of light travel in perfectly straight lines until they are refracted by the glass, causing them to travel at a slightly different angle. When the rays pass through the opposite surface of the glass, they are refracted again. If the sides of the piece of glass are parallel to one another, as in a window pane, the light emerges from the far side of the glass at the same angle at which it entered, having shifted only slightly to one side. If the light rays enter the glass perpendicular to the surface, however, the angle does not change at all.
A lens is a piece of glass that has been shaped with a very specific curve on each side. Light rays that enter the lens on one side emerge from the other side bent so that they converge at the focal point, some distance away from the center of the lens. That distance is the focal length of the lens, and it is dependent on the degree of curvature of both sides of the lens.
The focal length (f) of a thin lens can be determined experimentally by using the lens to focus an image of an object or light source on a screen. Measure the distance from the object to the lens (do) and the distance from the lens to the image on the screen (di), then calculate:
This is an approximation rather than an exact formula, but it is reasonably accurate for a lens whose thickness is insignificant compared to its radius of curvature. It does not work for lenses of a non-negligible thickness.
If one or both surfaces of a lens curve outward, as in an ordinary magnifying glass, the lens is called convex or biconvex, respectively. A sharp image will be observed at the focal point of a convex lens. If one or both of the surfaces curve inward, the lens is concave or biconcave. Light rays passing through a concave lens diverge, or spread apart, instead of converging. The focal point of a concave lens is on the near side of the lens, where the diverging rays would come together if they were traced backward, and the focal length is given as a negative value. There is a virtual image at the focal point, rather than the real, clear image at the focal point of a convex lens. By combining convex and concave lenses, very large degrees of magnification can be achieved. This technique is used in powerful telescopes and optical microscopes.
Sample Problem
A thin biconvex lens is placed 50.0 centimeters (cm) in front of an object. It projects a sharp image of the object on a screen 35.6 cm away. What is the focal length of the lens?
Answer
The focal length of a thin lens can be calculated according to the following formula:
Plug in 50.0 cm for the distance from the object (do) and 35.6 cm for the distance from the image (di):
Rearrange the formula to solve for f, then calculate:
The focal length is approximately 20.8 cm.
Circle of Confusion
Lenses are typically imperfect in various ways. Thus, the focal point is not so much an actual point as it is a small circle, because the light rays coming through the lens do not all converge in exactly the same place. This actual imperfection of the theoretical focal point is called the circle of confusion, or sometimes the "blur spot." Because of the limitations of human visual acuity, however, the circle of confusion is usually not a problem. In fact, there is a range on either side of the focal point where the image through a lens appears sharp to the human eye. This range is sometimes also called the "circle of confusion," or sometimes the "circle of least confusion." It is important in photography for determining depth of field, the nearest and farthest points in an image that appear acceptably sharp.
Bibliography
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Ersoy, Okan K. Diffraction, Fourier Optics, and Imaging. Hoboken: Wiley, 2007. Print.
Ghatak, Ajoy. Optics. 5th ed. New Delhi: McGraw, 2012. Print.
Laikin, Milton. Lens Design. 4th ed. Boca Raton: CRC, 2007. Print.
"Reflection, Refraction, and Diffraction." The Physics Classroom. Physics Classroom, 2015. Web. 28 July 2015.
Sharma, K. K. Optics Principles and Applications. Burlington: Academic, 2006. Print.